A homopolymer of 4-methylpentene-1 is a lightweight resin excellent in transparency. It is known that transparency of the 4-methylpentene-1 homopolymer can further be improved by modifying with a small amount of a straight chain .alpha.-olefin having from 5 to 18 carbon atoms as disclosed in Japanese Patent Publication No. 22077/75.
In general processes for producing 4-methylpentene-1 polymers by slurry polymerization, only a powdery polymer which is insoluble in a polymerization solvent is separated and recovered as a product. Recovery of both a solvent-insoluble polymer and a solvent-soluble polymer requires complicated procedures and entails high cost.
Conventional processes for producing random copolymers comprising 4-methylpentene-1 and a minor proportion of other .alpha.-olefin produce a solvent-insoluble polymer in a low yield as compared with the case of producing a 4-methylpentene-1 homopolymer, resulting in higher production cost.